What is the integral from-9 to 0 of 2+sqrt(81-x^2) ?

The integral from-9 to 0 of 2+sqrt(81-x^2) is 18+(81pi)/4

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integral from-9 to 0 of 2+sqrt(81-x^2)

\int_{- 9}^{0} 2 + 81 - x^{2} d x

18 + \frac{81 π}{4}

Decimal Notation

81.61725 \dots

Solution steps

\int_{- 9}^{0} 2 + 81 - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 9}^{0} 2 d x + \int_{- 9}^{0} 81 - x^{2} d x

\int_{- 9}^{0} 2 d x = 18

\int_{- 9}^{0} 81 - x^{2} d x = \frac{81 π}{4}

= 18 + \frac{81 π}{4}

\int \frac{- x - 1}{x ^{2} + 1} d x

\frac{\partial}{\partial y} (2 x + y^{2})

f (x) = x^{3}, 0, 4

y^{^{'}} - 3 y = - 6 y^{3}

\int_{0}^{1} \frac{4}{1 - x ^{2}} d x

What is the integral from-9 to 0 of 2+sqrt(81-x^2) ?
The integral from-9 to 0 of 2+sqrt(81-x^2) is 18+(81pi)/4